Question
Answer
$$(6x-8)(4x+2)(x-4)=24x^3-116x^2+64x+64$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(6x-8)(4x+2)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(24x^2+12x-32x-16)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(24x^2-20x-16)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}24x^3-96x^2-20x^2+80x-16x+64 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}24x^3-116x^2+64x+64\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{6x-8}\right) $ by each term in $ \left( 4x+2\right) $. $$ \left( \color{blue}{6x-8}\right) \cdot \left( 4x+2\right) = 24x^2+12x-32x-16 $$ |
| ② | Combine like terms: $$ 24x^2+ \color{blue}{12x} \color{blue}{-32x} -16 = 24x^2 \color{blue}{-20x} -16 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{24x^2-20x-16}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{24x^2-20x-16}\right) \cdot \left( x-4\right) = 24x^3-96x^2-20x^2+80x-16x+64 $$ |
| ④ | Combine like terms: $$ 24x^3 \color{blue}{-96x^2} \color{blue}{-20x^2} + \color{red}{80x} \color{red}{-16x} +64 = 24x^3 \color{blue}{-116x^2} + \color{red}{64x} +64 $$ |
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